Sanchez was not part of the squad that flew from Manchester Airport to Los Angeles on Sunday due to a 'personal administrative issue', which related to a visa.
The former Arsenal attacker had previously been handed a 16-month prison sentence for tax fraud, which saw the US government deny him a visa.
Sanchez has now given a positive update on the situation from Carrington, with the 29-year-old posting an image with a caption which suggested that he would soon board a flight to the US.
"The last training in Manchester. Soon [American flag]", read the selfie caption.
United will begin their pre-season preparations with a clash against Club America on July 20, before facing San Jose Earthquakes on Sunday night ahead of their first International Champions Cup match with AC Milan on July 26.